Topological data analysis: How to quantify "holes" in your data and why?
summary
Pipeline uses persistent homology to turn point clouds into fingerprints: grow discs, record births/deaths, produce persistence diagram and vectorize with a persistence image. Implementation demos use goody.alpha complex → simplex tree → persistence, a persistence image rasterization, and simple PCA classification (100 points per class gives clear separation). Other examples: sphere detection from 500 points (dimension‑2 feature), digits (8×8) using a loop length threshold >=8 to pick zeros/6/8/9, and finding a second‑highest peak in noisy signals.
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chapters (15)
- 0:00Introduction
- 0:49What is TDA
- 1:53TDA for spatial data
- 3:59Persistent homology for point clouds
- 7:49Persistence diagrams
- 9:11Point clouds to ML vectors
- 12:01Topological data analysis in Python
- 16:23Vectorizing persistence diagrams
- 20:19Shape detection in point clouds
- 25:00TDA for raster images
- 27:10Persistence for images
- 30:39Loop detection in digits
- 34:57Peak finding in signals
- 37:03Resources
- 38:29Q&A
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